Did Queen Elizabeth never sign the death warrant of Mary Queen of Scots?

History tells us that Queen Elizabeth signed the death warrant for Mary Queen of Scots, but told her secretary William Davison not to part with the document. Queen Elizabeth suggested on several occasions that Mary should be executed in some more secret way and, frankly, did not want another Queen's blood on her hands. She had Mary Queen of Scots in confinement for almost 20 years because she was hesitating to do anything drastic. History continues to say that Lord Burghley and the privy council decided to carry out the sentence at once and executed Mary on 8th February 1587. Queen Elizabeth was indignant when she received the news of the execution. She directed her wrath on Davison asserting that he did not follow her instructions to hold onto the document. Davison was tried, fined heavily, imprisoned, but later released. The Queen refused to employ him again and he died in 1608 after retiring to Stepney.
Francis Bacon had written a play in cypher called "The Historical Tragedy of Mary Queen of Scots" which contradicts the history books by saying that she did not sign the death warrant at all. An excerpt from this play is as follows:

Act V, Scene 1.--Palace of the Queen, Elizabeth and train.
     Q.E. "Fie, what a slug is Warwick, he comes not To tell us whether they will that she shall die or no. Ah! In good time here comes the sweating lord." (Enter Warwick.)
He announces the decision of "guilty." Enter Lords of Council; they present Elizabeth the warrant for Mary's death. She does not sign it.
     Q.E. "My lord, I promise to note it cunningly; But here come the ambassadors of our brothers of France and Spain."
Enter ambassadors, who plead for the life of Mary.
Scene 2.--Street in London. Enter Burleigh and Secretary of the Queen (Davison); met by Leicester. All enter a public house.

Scene 3.--Private room; Burleigh and Leicester force the Secretary to forge the Queen's name to the warrant for Mary's execution.


So which is true? Did Elizabeth really sign the document but use Davison as the scapegoat? She feared that Spain and France would combine forces to overthrow her reign and the death of Mary would be an event to initiate such forces. One would have to closely examine this signature with a signature known to be Queen Elizabeth's to determine if this one was indeed forged.